Servers
Time Limit: 10 Seconds Memory Limit: 32768 KB
The Kingdom of Byteland decided to develop a large computer network of servers
offering various services.
The network is built of n servers connected by bidirectional wires. Two servers
can be directly connected by at most one wire. Each server can be directly connected
to at most 10 other servers and every two servers are connected with some path
in the network. Each wire has a fixed positive data transmission time measured
in milliseconds. The distance (in milliseconds) delta(V, W) between two servers
V and W is defined as the length of the shortest (transmission time-wise) path
connecting V and W in the network. For convenience we let delta(V, V ) = 0 for
all V.
Some servers offer more services than others. Therefore each server V is marked
with a natural number r(V), called a rank. The bigger the rank the more powerful
a server is.
At each server, data about nearby servers should be stored. However, not all
servers are interesting. The data about distant servers with low ranks do not
have to be stored. More specifically, a server W is interesting for a server
V if for every server U such that delta(V, U) <= delta(V, W) we have r(U)
<= r(W).
For example, all servers of the maximal rank are interesting to all servers.
If a server V has the maximal rank, then exactly the servers of the maximal
rank are interesting for V . Let B(V) denote the set of servers interesting
for a server V.
We want to compute the total amount of data about servers that need to be stored
in the network being the total sum of sizes of all sets B(V). The Kingdom of
Byteland wanted the data to be quite small so it built the network in such a
way that this sum does not exceed 30n.
Write a program that:
> reads the description of a server network from the standard input,
> computes the total amount of data about servers that need to be stored
in the network,
> writes the result to the standard output.
Input
In the first line there are two natural numbers n, m, where n is the number
of servers in the network (1 <= n <= 30,000) and m is the number of wires
(1 <= m <= 5n). The numbers are separated by single space.
In the next n lines the ranks of the servers are given. Line i contains one
integer ri (1 <= ri <= 10) - the rank of i-th server.
In the following m lines the wires are described. Each wire is described by three numbers a, b, t (1 <= t <= 1000, 1 <= a, b <= n, a != b), where a and b are numbers of the servers connected by the wire and t is the transmission time of the wire in milliseconds.
Process to the end of file.
Output
The output consists of a single integer equal to the total amount of data about servers that need to be stored in the network.
Sample Input
4 3 2 3 1 1 1 4 30 2 3 20 3 4 20
Sample Output
9 because B(1) = {1, 2}, B(2) = {2}, B(3) = {2, 3}, B(4) = {1, 2, 3, 4}.Submit
Source: Southwestern Europe 2002